A genetic programming approach for delta hedging

Abstract

In this paper, using high-frequency intra-daily data from the UK market, we employ genetic programming (GP) to uncover a hedging strategy for FTSE 100 call options, hedged using FTSE 100 futures contracts. The output from the evolved strategies is a rebalancing signal which is conditioned upon a range of dynamic non-linear factors related to market conditions including liquidity and volatility. When this signal exceeds threshold values during the trading day, the hedge position is rebalanced. The performance of the GP-evolved strategy is evaluated against a number of commonly used, time-based, deterministic hedging strategies where the hedge position is rebalanced at fixed time intervals ranging from 5 min to 1 day. Assuming the delta hedger pays the bid-ask spread on the futures contract whenever the portfolio is rebalanced, this study finds that the GP-evolved hedging strategy out-performs standard, deterministic, time-based approaches. Empirical analysis shows that the superior performance of the GP strategy is driven by its ability to account for non-linear intra-day persistence in high frequency measures of liquidity and volatility. This study is the first to apply a GP methodology for the task of delta hedging with high frequency data, a significant risk management issue for investors and market makers in financial options.